A square cavity with a side length of L°= 1e-3° m is filled with water
(density: 1000 kg/m3, dynamic viscosity: 1e-3 kg/m/s). The
upper wall is moved with a constant velocity U0 imposing a rotational
movement of the fluid in the cavity. Here, the configurations with Re°=°100,
Re°=°1000 and Re°=°10000 are simulated by adjusting the velocity of the lid
correspondingly. The highly-resolved Finite-Difference calculations by Ghia et
al with a grid resolution of 257x257 are taken as
reference.
Numerical Setup
Three different resolutions of 50x50, 100x100, and 200x200 fluid particles are used
for each Reynolds-Number. Figure 1 shows the initial particle distribution for the coarsest
resolution where wall boundary conditions are imposed by three rows of particles.
The simulation is run until a fully developed flow is achieved.
Figure 1. Initial Particle Distribution of the 50x50 Case
Results
The velocity profiles in the horizontal and vertical centerlines are shown in Figure 2 to Figure 4 for each
Reynolds-Number. For the Re = 100 case, all the profiles show very good agreement
with the reference profiles by Ghia et al. Velocity profiles at Re = 1000 and Re =
10000 match those of Ghia et al at finer resolutions of 100x100 and 200x200,
respectively. This is expected as higher Reynolds numbers results in finer
structures and requires more particles to resolve.
Figure 2. Profiles of the Re=100 Case
Figure 3. Profiles of the Re=1000 Case
Figure 4. Profiles of the Re=10000 Case
S. Adami, H. Hu and N. Adams, "A generalized wall
boundary condition for smoothed particle hydrodynamics," Journal of
Computational Physics, vol. 231, pp. 7057-7075, 2012.
U. Ghia and K. S. C. Ghia, "High-Re solutions for
incompressible flow using the Naview-Stokes equations and a multigrid method,"
Journal of Computational Physics, vol. 48, pp. 387-411, 1982.
